期刊
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
卷 31, 期 2, 页码 133-151出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10652469.2019.1681991
关键词
Orthogonal polynomials; bispectral orthogonal polynomials; recurrence relations; Krall polynomials; Laguerre polynomials
资金
- Ministerio de Ciencia, Innovacion y Universidades [PGC2018-096504-B-C31]
- Junta de Andalucia [FQM-262]
- Feder Funds (European Union)
- PAPIIT-DGAPAUNAM (Mexico) [IA102617, IN104219]
- CONACYT (Mexico) [A1-S-16202]
We study the bispectrality of Laguerre type polynomials, which are defined by taking suitable linear combinations of a fixed number of consecutive Laguerre polynomials. These Laguerre type polynomials are eigenfunctions of higher order differential operators and include, as particular cases, the Krall-Laguerre polynomials. As the main results, we prove that these Laguerre type polynomials always satisfy higher order recurrence relations (i.e. they are bispectral). We also prove that the Krall-Laguerre families are the only polynomials which are orthogonal with respect to a measure on the real line.
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